To a large extent, humans' interactions with electronic devices, such as computers, tablets, and mobile phones, requires physically manipulating controls, pressing buttons, or touching screens. For example, users interact with computers via input devices, such as a keyboard and mouse. While a keyboard and mouse are effective for functions such as entering text and scrolling through documents, they are not effective for many other ways in which a user could interact with an electronic device. A user's hand holding a mouse is constrained to move only along flat two-dimensional (2D) surfaces, and navigating with a mouse through three dimensional virtual spaces is clumsy and non-intuitive. Similarly, the flat interface of a touch screen does not allow a user to convey any notion of depth. These devices restrict the full range of possible hand and finger movements to a limited subset of two dimensional movements that conform to the constraints of the technology.